The importance of water and hydraulic pressure in cell dynamics

While the precise mass fraction of water in the cell cytoplasm probably depends on the cell type, water is universally the most abundant molecule in the cell. The next most abundant cytoplasmic components (in terms of overall number and concentrations) are ions: K⁺, Na⁺, Cl⁻, H⁺, HCO₃⁻, PO₄⁻ and Ca²⁺ (Fig. 1). Small molecules, such as ATP, taurine, amino acids and glucose are next, and only then do we reach macromolecules, such as proteins and genetic material. A detailed discussion of quantitative estimates of cell components is given in an excellent book (Milo and Phillips, 2015). However, an immediate question following this observation is, why this particular overall composition? Given that nothing in biology makes sense except in the light of evolution, it is reasonable to assume that this composition is similar to the primordial environment where life first evolved. Indeed, there are good reasons to believe that the proto-cell developed in the specialized environment of volcanic pools with high concentrations of K⁺ (Mulkidjanian et al., 2012). The operations of essential proteins of life, including the ribosome, DNA polymerase and RNA polymerase, appear to require high concentrations of K⁺. Life went to the Na⁺-rich ocean environment and became global when the proto-cell developed the Na/K exchanger. The Na/K exchanger is an active ion pump (ATPase) that exports three Na⁺ and imports two K⁺ ions, and maintains high K⁺ and low Na⁺ levels in the cytoplasm (Gadsby, 2009). It is one of many active ion exchangers that helps to maintain the ionic composition of the cytoplasm. Therefore, the ionic content of the cytoplasm is actively regulated by the cell, which ultimately impacts critical biochemical processes such as protein translation (Rozov et al., 2019), as well as biophysical features, such as cell size, cell shape and cell motility.

By varying degrees, the plasma membranes of many mammalian cells are permeable to water (Reuss, 2012; Farinas and Verkman, 1996; Farinas et al., 1997). Owing to free-energy driving forces arising from the entropy of mixing, solutes, such as ions, molecules and proteins, generate an osmotic pressure, which drives the flow of water from regions of lower solute concentration to regions of high solute concentration (Atkins, 1990; Reichl, 2016). At physiologically relevant solute concentrations (<1 M), the osmotic pressure is proportional to the solute concentration (as defined by van't Hoff's equation): Π=γRTc, where c is the solute concentration in molars and R is the gas constant, T is the temperature and γ is an activity coefficient that corrects for non-ideal behavior (but is generally close to 1) (Atkins, 1990). In physiology, osmotic pressure generated by macromolecules (proteins and polymers) is also called the oncotic pressure and is responsible for maintaining water content in circulatory systems such as the vasculature (Mitchison, 2019). It is important to note that the osmotic pressure is conceptually different from the hydraulic (or hydrostatic) pressure, which drives water away from regions of high water density. These two pressures oppose each other, and at chemical equilibrium, the free energy per water molecule is equal across the permeable cell membrane, and the osmotic pressure difference is equal to the hydraulic pressure difference (Fig. 1). The osmotic pressure or entropy of mixing also has nothing to do with any attractive interaction between water and solutes (Jaynes, 1992). Fundamentally, osmotic pressure is an entropic force derived from the ability to distinguish different types of objects in the system (Jaynes, 1992). Given that the cell must maintain high K⁺ and low Na⁺ concentrations, there is a continuous exchange of Na⁺ with K⁺ and their associated negative ions even when the overall solute concentration in the cytoplasm is constant (pump and leak) (Hoffmann et al., 2009). Therefore, ion concentrations are never in equilibrium. There is always a concentration gradient of Na⁺ and K⁺ across the cell boundary.

Here, fundamental unanswered questions are what sets the overall solute concentration, ionic content and water content in the cytoplasm, and does the cytoplasmic composition change depending on cell type, cell cycle and/or environmental variables? Ion fluxes of channels, transporters and pumps and their dependence on ion concentration, transmembrane voltage, available ATP, membrane tension and other factors, such as Ca²⁺, are sometimes known (Yellin et al., 2018; Li et al., 2015; Russell, 2000). Therefore, it may be possible to model this system of ion homeostasis mathematically. Indeed, models of this cell volume (i.e. the cell water and/or ion content) control system were first developed for red blood cells in the 1960s and have since been extended, modified and analyzed in many studies (Tosteson and Hoffman, 1960; Weinstein, 1992; Jakobsson, 1980; Mori, 2012; Armstrong, 2003; Jiang and Sun, 2013). These models, collectively known as pump-leak models, can explain the general characteristics of cell volume and ionic concentration homeostasis at short time scales. However, cell volume is also regulated dynamically during cell growth and division, or in response to external environmental changes such as osmotic stress (Hoffmann et al., 2009). The mechanisms by which this happens must involve a means for the cell to sense its volume, together with multiple feedback mechanisms that allow the cell to modulate its solute content and active tension. These mechanisms are beginning to be elucidated, but they are still poorly understood. For example, a change in cell water and/or ion content alters the cytoplasmic hydraulic pressure, which impacts the cortical stress (Stewart et al., 2011). Changes in ion content and Ca²⁺ fluxes may also modulate cytoskeletal processes and active contraction in the cortex (He et al., 2018; Zhao et al., 2019). These elements are somehow combined to establish a steady state where cell hydraulic pressure, water content, volume, pH and ionic composition are maintained. For most mammalian cells, which do not have cell walls, the numerical value of ΔP appears to range from a few hundred to a few thousand pascals (Petrie et al., 2014; Sao et al., 2019; Perez-Gonzalez et al., 2019). For bacteria, fungi and plant cells, ΔP (the turgor pressure) can approach megapascal values (Sun and Jiang, 2011; Beauzamy et al., 2015; Altenburg et al., 2019). There is also evidence that the hydraulic pressure difference, ΔP, depends on the cell type and signaling pathway activity. For example, when YAP1, a downstream effector of the mechanosensitive Hippo signaling pathway that controls organ size and cell growth, is knocked out, the cytoplasmic pressure is significantly lower (Perez-Gonzalez et al., 2019).

The intracellular and extracellular ionic composition, together with the types of ion channels present on the membrane, sets the resting membrane voltage (Yellin et al., 2018; Ermentrout and Terman, 2010). This membrane potential, which is defined as the intracellular voltage minus the extracellular voltage, results from a charge imbalance across the cell membrane capacitor. The membrane capacitance is very small, thus only a very small charge imbalance is needed to create a membrane potential; the cytosol as a whole can safely be considered electroneutral. The resting membrane potential is generated primarily by two factors: (i) a high intracellular K⁺ concentration with respect to the outside, generated by the Na/K pump, and (ii) the presence of passive K⁺ channels on the membrane (and the relative absence of other channels). High intracellular K⁺ concentration and high K⁺ permeability of the membrane system leads to the diffusion of K⁺ out of the cell, until the intracellular side has a voltage negative enough with respect to the extracellular space to counterbalance this diffusive tendency. Typical values of the cell membrane voltage range from −50 to −90 mV; this depends on the cell type and reflects the differing ionic concentrations and compositions with regard to ion channels and pumps (Yang and Brackenbury, 2013; Yellin et al., 2018). The resting membrane potential seems to correlate with the differentiation state of the cell, and is also known to fluctuate with the cell cycle (Yang and Brackenbury, 2013). The significance of these observations is unknown, but may be linked to water flow and cell volume regulation, which are the focus of this Review.

The cytoplasmic osmotic pressure can vary spatially in the cytoplasm because cells are generally polarized, even in the absence of any external gradients; this means that ion channels, transporters and pumps that modulate ionic concentrations are typically not uniformly distributed on the cell surface. A simple 1D diffusion calculation predicts that if there is a solute influx, I, at the cell leading edge and the opposite solute efflux at the trailing edge and the solute is free to diffuse in the cytoplasm, the solute gradient would be I/D in the cell where D is the solute diffusion coefficient. However, with the exception of a few cases, precise measurements of intracellular ion concentration gradients are lacking (Zeuthen, 1978; Tsien, 1989). Therefore, locally, the ion concentration and osmotic pressure may deviate from the overall average of ∼300 mM. Such concentration changes can be small and be less than 1 mM. However, a concentration of 0.5 mM is equivalent to ∼300,000 solute molecules per 1 μm³ or 1 fL. Given that some ion channels and pumps can allow the passage of ∼10⁶ ions per second (Gadsby, 2009; Shieh et al., 2000), only a few of these can generate this kind of concentration changes quickly.

The cytoplasm is also a viscous liquid that contains a fluid-like cytoskeletal network. The central role of the cytoskeleton in cell motility has been studied extensively (Pollard and Borisy, 2003; Mogilner and Oster, 1996). Indeed, there are thousands of papers that describe the role of actin in driving cell movement and cell shape changes in general. It is well known that actin filaments, together with actin-binding proteins and myosin assemblies, form a viscous gel-like fluid that extends and contracts, depending on the local rates of actin polymerization and depolymerization, and the amount of myosin contraction (Fletcher and Mullins, 2010; Murrell et al., 2015). Therefore, the cytoplasm is filled with at least two types of fluid (Li and Sun, 2018) – the cytosol, which is the combination of water, ions, organic molecules and proteins, and the cytoskeleton, which consists of actin, microtubules and intermediate filaments. These two fluids can be considered as two fluidic phases (with two different pressures) that can dynamically interact. For the cytoskeletal phase, the network pressure can be estimated by the equation of state for the network (pressure–material density relationship; for example, the ideal gas law PV=nRT).  For liquids, gels and polymers, the equation of state is more complex (Rowlinson and Widom, 1982). Any active contractile stresses (such as those from myosin and crosslinking proteins) will modify the equation of state. Again, at steady state where there is no flow, force balance would require that any pressure gradients in the cytoskeleton phase must be balanced by hydraulic pressure gradients. This may be the reason why contractions (or ‘negative’ pressure) within the F-actin network can generate hydraulic pressure and result in the development of cell blebs (Charras et al., 2005; Charras et al., 2008; Charras et al., 2009), although fluid flow from outside into the cell might also contribute to blebs (Taloni et al., 2015). This may also explain why the measured cytoplasmic hydraulic pressure depends on myosin activity (Sao et al., 2019). Recent papers have demonstrated that flows in the two fluidic phases can generate forces to position organelles, such as the nucleus and the spindle, in the cell cytoplasm (Duan et al., 2020; Deneke et al., 2019). There are also other fluidic phases, such as the mitochondrial network, lipid reservoirs and nucleoli, which consist of molecules that are phase-separated from the cytosol and the cytoskeleton, and which behave as another viscous liquid; these combine to define the overall mechanical state of the cell.

where θ_n,cytosol are the volume fractions of the network phase and cytosol phase, respectively. The local flux of water is determined by the local hydraulic and osmotic pressures, that is ⁠, and therefore depends on local ion channel activity. Actin polymerization flux J_n is controlled by actin nucleators, signaling pathways and also mechanical forces (Footer et al., 2007; Parekh et al., 2005; Mogilner and Oster, 2003; Hirata et al., 2008). The remaining unknowns are the cytoplasmic flow velocities and their respective volume fractions. These velocities are determined by the mechanics of the fluidic phases and forces that develop in these systems as well as potential active network forces, such as myosin contraction (Li and Sun, 2018; Li et al., 2019; Mogilner et al., 2018; Keren et al., 2009).

When examining the extension of the cell boundary during motility (Fig. 2), it is interesting to also contemplate the motion of the plasma membrane. During cell translocation, the membrane can be stationary with respect to the cell, that is, move with the same speed as the cell, or it can be stationary with respect to the lab-frame and treadmill forward. A third possibility is a tank-treading motion where the flow of the apical membrane velocity is forward and that of the basal membrane is reverse. Indeed, vesicle trafficking can facilitate treadmilling of membrane forward (O'Neill et al., 2018), whereas forces owing to friction with the substrate can slow down the movement of the basal membrane. These different types of membrane flow behavior have been measured in migrating cells (Lee et al., 1990; Traynor and Kay, 2007; Kucik et al., 1989; Dai and Sheetz, 1995). There does not appear to be a significant flow of membrane with respect to the cell during cell migration. It is also known that mechanical behavior of the membrane is critical for cell polarization and cell motility (Shi et al., 2018; Houk et al., 2012; Keren et al., 2009). Indeed, membrane tension has been shown to serve as a global inhibitory signal for protrusion, which coupled to local activation, leads to cell polarity (Houk et al., 2012). In addition, in the absence of any chemotactic signals, Ca²⁺ currents through membrane channels are also essential for spontaneous cell polarity (Wei et al., 2009).

Eqn 3 implies that cells can move by either actin polymerization or water flux. Indeed, there is experimental evidence that actin is dispensable during migration under confinement (Balzer et al., 2012; Stroka et al., 2014b; Panopoulos et al., 2011). For instance, in narrow, confined microfluidic channels, mouse S180 fibrosarcoma cells with a depolymerized actin network are able to migrate with the same speed as cells with an intact cytoskeleton, whereas other cell types (human metastatic MDA-MB-231 breast cancer cells) show a reduction in cell speed, but continue to move even after actin is completely depolymerized (Stroka et al., 2014b). In microchannels, MDA-MB-231 cells show a polarized distribution of aquaporins and NHE1 (a Na and H exchanger; Putney et al., 2002). Moreover, if the osmolarity of the external medium at the leading and trailing ends of the cell are perturbed independently, different cell speeds and cell boundary velocities are observed (Stroka et al., 2014a). Cells retained their asymmetrical distribution of ion transporters (NHE1 and potentially others) after the disruption of the actin network; at the leading end, the cell is passaging ions (perhaps mostly Na⁺ and Cl⁻) into the cell, whereas at the trailing end, the cell is transporting ions out of the cell. This constant flux of ions establishes a slight gradient of solute concentration in the cell and therefore generates a constant flux of water through the cell. This transport of water leads to a forward translocation of the cell body in this so-called osmotic engine model (OEM) of cell migration (Fig. 2B) (Stroka et al., 2014b; Shoji and Kawano, 2019; Hoffmann et al., 2009). Another parallel mechanism is the uptake of water not through the membrane, but through micropinocytosis (Moreau et al., 2019). In this case, large endocytic vesicles containing extracellular fluid are taken up by the cell, which also leads to cell movement in confined channels.

The remaining question is why the cell uses water-driven mode of motility in confined channels. One possibility is that the geometry of thin longitudinal channels facilitates the polarization of aquaporins and ion channels and/or pumps. Also, in 2D, water is free to move around the cell while, in confined channels, water cannot easily flow around the cell and instead must go through the cell. The different speeds of cells in the absence of actin polymerization suggests that the relative contributions of actin and water to cell speed depends on cell type; therefore, the question arises as to what is the determining factor for a cell to switch between the actin- and water-based mode of cell migration. Accumulating recent experiments suggest that cells are sensitive to the hydraulic resistance they experience (Prentice-Mott et al., 2013; Zhao et al., 2019; Srivastava et al., 2020; Moreau et al., 2019). Hydraulic resistance is the effective fluidic resistive force the cell experiences as it moves (Li and Sun, 2018; Prentice-Mott et al., 2013). If water does not flow through the cell, it must be pushed out of the way around the cell. This is easy to accomplish on flat 2D substrates where the hydraulic resistance, which is proportional to the water viscosity, is very low (Fig. 3). However, in confined channels, in order to push the water forward, the cell must push the entire column of water, which requires overcoming frictional forces between water flow and the channel walls. Therefore, the hydraulic resistance in confined channels is very high and is also proportional to the channel length (L in Fig. 3A) and the channel cross-sectional area (Fig. 3A). Based on theoretical modeling of a two-phase model of the cytoplasm, the cytosol flow velocity v_cytosol is directly related to the external hydraulic resistance (Li and Sun, 2018). Therefore, even for fixed J_water and J_n, the final cell speed depends on the hydraulic resistance. Indeed, as the hydraulic resistance increases, the contribution of J_water to cell speed increases. This provides a possible explanation for why cells can rely on OEM for motility inside confining channels with a high hydraulic resistance, as opposed to using actin in 2D (Li and Sun, 2018). This also indicates that the water-based osmotic engine is a polarized manifestation of the cell volume control system discussed in the Introduction. The same ion channels or pumps involved in maintaining the cell water and/or ion content, when positioned in a spatially polarized manner, also drive directional water influx and efflux, and OEM. Actin- and myosin-mediated contraction play prominent roles in cell polarization, and therefore indirectly influence J_water and OEM, pointing to a crosstalk between OEM and the cell cytoskeleton in cell motility. Modeling also indicates that higher metabolic costs are incurred in order for a cell to move by using OEM under high hydraulic resistance conditions than in 2D cell culture conditions (Li et al., 2019). This prediction agrees with the elevated cytoplasmic ATP concentrations measured in cells moving in collagen microchannels (Zanotelli et al., 2018). Moreover, cells in 3D matrices experience higher hydraulic resistance due to the porous nature of the ECM that prevents easy fluid flow (Maity et al., 2019). Here, the matrix fibers generate additional resistance to fluid flow, and higher matrix density can increase hydraulic resistance by several orders of magnitude (Fig. 3C; Maity et al., 2019). Therefore, OEM-based motility may be more prominent in these conditions.

Mechanically, the presence of high hydraulic resistance during migration also implies that the hydraulic pressure at the cell leading edge is different from the far-field ambient value (P_∞ in Fig. 3A). This is a consequence of the physics of viscous flows, where flow velocities are directly proportional to pressure gradients (Pozrikidis, 2011). If the cell in the channel is not transporting water through the cell, then the external fluid must also move forward at the same speed as the cell; this implies that there is a slightly higher pressure directly in front of the cell (P_f) than P_∞. This pressure gradient is proportional to the channel length. Indeed, recent experiments showed that when cells are exposed to different channels and hydraulic resistances, they exhibit a preference in the direction of their migration, usually preferring the channel with the lowest hydraulic resistance (Zhao et al., 2019; Pretice-Mott et al., 2013) (Fig. 3B). This means that the direction of cell movement is influenced by the hydraulic resistance, and possibly the hydraulic pressure immediately in front of the cell. This form of pressure sensing during migration is called barotaxis (Moreau et al., 2019). Indeed, when the mechanosensitive cation channel TRPM7 is either blocked or knocked out, cells lose their directional preference for channels with low hydraulic resistance and instead enter the channels with the largest cross-sectional area irrespective of their prevailing hydraulic resistance (Zhao et al., 2019). Chelating Ca²⁺ or blocking myosin II function has a similar effect on the migration direction. Along these lines, when cells on 2D surfaces are exposed to changes in hydraulic pressure of only a few pascals, their cytoplasmic Ca²⁺ levels show a strong response that is dependent on TRPM7 (Zhao et al., 2019; Liu et al., 2015). Therefore, cells are sensitive to the hydraulic resistance around them and make decisions to polarize in a Ca²⁺-dependent manner. This sensitivity is connected to hydraulic pressure external to the cell and is actively sensed.

Based on Eqn 1, hydraulic pressure is also linked to the cortical tension. When cells are subjected to external mechanical force, there is also an active response that depends on cellular Ca²⁺ dynamics (He et al., 2018). For example, when cells are mechanically compressed, Rho activity and myosin contraction have been found to instantly decrease in a Ca²⁺-dependent manner (He et al., 2018). In contrast, when cells are mechanically stretched, myosin contraction increases (Tao and Sun, 2015; Koride et al., 2014; Zhao et al., 2007; Luo et al., 2013). Furthermore, entry of cells into and their motility in short confining channels, which compresses and stretches cells in the apicobasal and longitudinal direction, respectively, results in elevated RhoA activity and myosin II contractility (Mistriotis et al., 2019). Moreover, when cells are subjected to sudden changes in hydraulic pressure, active responses by the cell are also observed (Ju et al., 2009; Stover and Nagatomi, 2007; Kao et al., 2017; Hui et al., 2014; Liu et al., 2019). These experiments, together with hydraulic resistance experiments in channels, indicate that cellular mechanosensation has a universal basis and involves membrane-tension-sensitive ion channels and Ca²⁺ currents, as well as myosin and its associated pathways. Ca²⁺, as a secondary messenger, also affects many passive and active ion channels (Ranade et al., 2015). Therefore, the same cell volume regulation system that controls cellular ion and water homeostasis is likely to regulate OEM, as well as cell polarization and the hydraulic response.

Active transport of water that underlies OEM-based cell migration and cell volume regulation is also prominent during tissue development and morphogenesis (Leonavicius et al., 2018; Latorre et al., 2018). For instance, the kidney is a specialized organ that is responsible for retaining 99% of the water in the body. Kidney epithelial cells in the proximal tubule are responsible for this water reabsorption activity and act by pumping Na⁺ and Cl⁻ ions across the epithelium (Weinstein, 2000). The molecular details of this machinery are partially understood. This water-absorption machinery involves ion channels and pumps, and is broadly the same as those driving OEM, but the control mechanisms are likely to be different. Since OEM is predicted to drive cell movement and movement is related to forces, theoretical calculations suggest that is there is also mechanical force generation during the passaging of water across the kidney epithelium (Choudhury et al., 2019 preprint) (Fig. 4). Indeed, this force, in the form of an apical–basal hydraulic pressure difference, was quantified for kidney epithelium using a permeable microfluidic method (Choudhury et al., 2019 preprint). Similarly, MDCK II cells grown on impermeable substrates can generate dynamic fluid-fill domes (Yang et al., 2019). These domes are generated from active pumping of water across the epithelium into the domes, and according to OEM predictions, the hydraulic pressure is higher inside the dome. This elevated hydraulic pressure can drive epithelial shape changes, that is, morphogenesis.

The active pumping of water, therefore, is another way for cells to generate mechanical force that is transverse to the epithelium. The elevated pressure at the back of the cell is effectively a pushing force and can promote tissue expansion. For instance, during early mammalian development, a cluster of cells called the blastocyst must expand and develop a lumen to burst out of the zona pellucida, a shell surrounding the early embryo (Leonavicius et al., 2018). This lumen expansion has been shown to rely on elevated pressure inside the lumen. Another example is the mammary gland organoid; here, expansion of the organoid in the matrix and generation of a fluid-filled lumen also requires an elevated pressure (Yang et al., 2019). The elevated pressure is not particularly high – of the order 100–300 Pa, which is about 0.1–0.3% of the atmospheric pressure. However, after multiplying by the typical cell surface area, this pressure difference translates to a force of 50–100 nN per cell. This force is similar to traction force generated by actomyosin contraction (Style et al., 2014; Wang and Li, 2009). Therefore, the OEM model of pressure and/or force generation might be as significant as actomyosin contraction with regard to force generation.

Furthermore, the same kinematic conditions that drive cell boundary movement (see Fig. 2A) are also relevant in tissues during the collective movement of a group of cells. If the epithelium is mature and cells have established junctional complexes such as gap junctions (Kumar and Gilula, 1996; Nielsen et al., 2012), the cytoplasm of neighboring cells are directly connected. Fluid, ions and other molecules from one cell can flow into neighboring cells connected by gap junctions (Fig. 5). This flow of material will drive the movement of the cell–cell boundary and thus the relative movement of cells with respect to each other. Here, pressure differences in neighboring cells, both with regard to osmotic and hydraulic pressure, can drive this flow and contribute to cell collective motion. Therefore, water flows and hydraulic pressures generated by ion fluxes are also important in tissue morphodynamics, and can be used by cells collectively to generate forces and movement.

Water is a central molecule of life and an essential component of the cytoplasm. When water is free to flow in and out of the cell, its overall cytoplasmic content must be carefully controlled. Since water follows solute transport, the cell controls its water content by controlling its solute concentration. Moreover, it is reasonable to conjecture that the cell controls the concentrations of all of the essential ions of life, including K⁺, H⁺ and Ca⁺, so that there is a consistent chemical environment for proteins. The combined homeostatic system can achieve constant ion concentrations and a constant cell volume for a given protein and amino acid content. Indeed, simple modeling shows that within such a system, protein and amino acid concentrations are also constant, therefore as the cell grows by increasing protein content, the cell volume increases proportionally with protein content (Tao and Sun, 2015; Yellin et al., 2018).

This system of cell volume and ion content control is also likely responsible for the observed behaviors when cells are subjected to external force, changes in hydraulic pressure or changes in external osmolarity (Tao and Sun, 2015). External pressure and osmolarity changes will directly cause water flux across the cell membrane. Pressure changes and external forces will also influence the force balance at the cell cortex, and likely result in activation of mechanosensitive ion channels, giving rise to a possible feedback system. Any changes in the force balance at the cell surface, for instance from an externally applied force, can activate a multitude of molecules and cell signaling responses. In particular, with regard to ion homeostasis, many of the ion channels are also Ca²⁺ dependent. Furthermore, most mechanosensitive channels, such as transient receptor potential channels (TRPs) are also Ca²⁺ channels (Bouron et al., 2015; Clapham et al., 2001; Venkatachalam and Montell, 2007), implying that Ca²⁺ dynamics could ‘encode’ the ‘control language’ of a cell. Ca²⁺ is also required for spontaneous polarization of the cell (Wei et al., 2009) and controls the activity of many ion channels and pumps, as well as regulating cytoskeletal dynamics. What the roles of Ca²⁺ are is an important open question for cell mechanics, and fully elucidating this in cells may be a key to better understanding of cell volume regulation, ion homeostasis and cell mechanosensation.

Another open area that requires more investigation is the interplay between the F-actin phase and the water phase. We have discussed that the F-actin network can mechanically interact with the cytoplasmic fluid, and their relative flow velocities can set the cell boundary speed. But there are additional couplings as well. F-actin is known to be involved in establishing cell polarity, and spatially localization of ion channels or pumps that drive water movement is likely to depend on the cytoskeleton via the vesicular trafficking system. Moreover, processes such as macropinocytosis that also take up water involve the actomyosin machinery (Moreau et al., 2019). Therefore, water and cytoskeleton systems have many areas of potential interface, and elucidation of their crosstalk deserves further exploration.

Many important signaling pathways are linked to activities of ion channels, cytoskeleton and myosin in the cell cortex. For example, the Rho–Rac signaling pathway is integral for cell polarization and is connected to myosin contraction and cytoskeletal regulation (Maddox and Burridge, 2003; Jilkine et al., 2007; Amano et al., 1997; Hung et al., 2013). Cytoskeletal tension and activity also influence the Hippo signaling pathway and the nuclear localization of its downstream effectors, the transcription factors YAP and TAZ (Perez-Gonzalez et al., 2019; Meng et al., 2018; Perez-Gonzalez et al., 2018; Dupont et al., 2011), which modulate cell size and growth dynamics through their target genes (Tumaneng et al., 2012; Yu et al., 2015). We also know that there must be feedback from the Hippo pathway to the homeostasis system because the cytoplasmic pressure is lowered when YAP is knocked out (Perez-Gonzalez et al., 2019). The steady-state pressure in a cell should correspond to the net osmotic pressure and the total solute concentration. Therefore, the transcriptional activities of the Hippo pathway could also influence cell osmotic control. Beyond the Hippo signaling pathway, there are likely multiple Ca²⁺- and mechano-sensitive pathways, which lead to biochemical modifications and expression of transcriptional programs. Therefore, it is reasonable to postulate that signals arising from the volume and ion homeostasis system could also lead to global changes in cell behavior.

Finally, if the cytoplasmic osmotic and hydraulic pressure is mostly constant during the cell cycle, and the cell volume scales linearly with protein content, the volume regulation system provides a way for the cell to sense its size. From Eqn 1, we see that if the volume regulation system maintains a constant cell osmolarity and ΔP is constant, cell tension must scale with the radius of curvature. Therefore, a bigger cell with a larger radius of curvature will also have higher active tension. The active tension of the cell is mostly generated by myosin contraction. Based on quantitative single-cell measurements of the levels of phosphorylated myosin light chain (pMLC), a marker of cell active tension, the cell tension indeed appears to increase with cell size (Perez-Gonzalez et al., 2018). Moreover, varying cell substrate stiffness, which changes cell size, also results in corresponding changes in the total pMLC content of the cell. Therefore, the cell active tension in Eqn 1, together with the volume homeostasis system, could be a way for the cell to measure its size. Another cell-size-sensing mechanism that is based on the dilution of a fixed number of proteins has also been proposed (Schmoller et al., 2015). These mechanisms may work together to control cell size during cell cycle progression and generate a cell size checkpoint (Ginzberg et al., 2015; Kafri et al., 2013) that regulates cell growth rates and the G1-S transition. This cell size checkpoint may involve a combination of cell tension sensing, possibly through the Hippo pathway and other Ca²⁺-sensitive pathways and the dilution of key cell cycle proteins as suggested previously (Schmoller et al., 2015). Further investigations are needed in order to fully reveal the cellular pressure and volume control system and to understand its implications for cell growth and cell cycle control.